TECHNION - 'ISRAEL INSTITUTE COASTAL & MARINE

OF tECHNOLOGY ENGINEERING RESEARCÑ

HYDRAULICS LABORATORY INSTITUTE

REVIEW OF CURRENT PROCEDURES

### fo r

TOTAL SHIP DRAG CALCULATION

### at

### the

TECHNION TOWING TANK

P.N. 106/82

### by:

IRINA BOGUSLAVSKY, Ph.D.

TECHNION CITY - HAIFA July, 1982

CONTENTS

1. Acknowledgement.

.2. Abstract

Introduction

Methods of ship resistance determination from scale models

4.1 Thé conventional analysis of ship resistance 6

4.2.. Hüghesis method . TO

4.3 The method adopted in Technion Towing Tank (T..T.T. method) 13

44 Choice of model dimensions 1 5

4.5 "Trip Wire" pob1em _{19}

Approximate method of ship and model resistance _{calculation.} _{2i}

### 5j

_{Estimation of form factor}

. 21

5.2 Estimation of wave resistance .

24

.5,3 Calculation procedure 27

Examples forthe use of the I.T.T. method and comparisons With _{30}

othe' niethods of ship resistahce. calculation

6.1 Available data .

30
6.2 Ship "Hebe" resistance calculations using TT.î..iiiethod _{31}
6.3 _{Comparison of resistance calculation methods Using the}

3g data of the French and the Technion models

6.4 _{Cornparisión of the I.T.T. metho.d with .the "Victory."}

40

ship model tests . . .

### I

PAGE

. Conclusiofl

8. Appendix I: Procedures of ship resistance calculations úsing the T.T.Ï. method.

References 10. tables PAGE 43 44 47 49

LIST OF TABLES

PAGE

Table .1 - Charactéristics of the prototype "Hebe" and its 50 models..

Table .2 CalculatiOn of "Trip Wire" resistançecoefficient 51

for Teçhn.ion model.

Table 3 - Computation of wave resistance coefficiént and n 52 form coefficient for Technion. model by T.T.T.. :metbod.

Table 4. - Cornputatin of wave resistance coefficient and r 53

form coefficient for French model by T T T method

Tablé 5- Calculation of total resistance forship "Heben by . 54 I.T.T. method using data of Technión and French

model trials.

Table 6 - Calculation of total resistance for hip "Hèb&' 55 using approximate method.

Table 7 - Calculation of total resistance fOr French model 56. using data .of Technion model and approximate

method.

Tablé 8 - Comparison f form coefficient n computed. for models 57

inwide range of Reynolds numbers using experimental

### :IJ5

OF ' FIGURES:PA6E

### Figure 1

### - The towing carriage

_{4}

### Figure. 2

### - 'The. model

_{attached to the carriage and measuring equipment}

_{4}

### Figure 3

### - Conventional method of ship resistance determination from

### scali 'models

_{7}

### Figure 4 '- Hughes'.s method' and method adopted in Technion TöwingTank

### (LT.T. method)' of' ship resistance detérminatlon from scale

### models

' 1:1

### Figure 5

_{Relative model size and Towing Tank}

_{versus the greatest}

### Fróu'de Number Which must be achièved

_{17}

### Figure 6'

### - Coefficient 'A

### versus the waterline bow angle

19### Figure 7

_{- Determination of T1-coèfflci'ént for turbulent 'flow about'.the}

### ship and módel body.

- .22### Figure 8

_{- Determination of}

_{coéfficient for modification of .Papmel 's}

### wavéresistance.'formula.

'' .25

### Figure 9'

_{- Computation of mOdel resistance'coèfficlènt by T.LT.}

### method using outcome

### f Techñion modei'tests'

_{32}

### Figure '10 - Computation of model resistance

_{coefficient by T.TT.}

### method using outcome 'of French'rnodel tests

_{32}

### Figure 1

_{- Total resistance dependence on speed'for ship 1tHebe"}

_{37}

### FiÒure '12 - Total resistance coefficient of models and ship "Hebe"

### (without 'rOúghness).

'' 38'

V

LIST OF SYMBOLS

- Displacement (ton) - Under-water volume (m3)

Am Midship section area (iii2)

B Breadth, Of model ôr ship at WL (,) b - Width of towing tank (rn)

CB - Block cOefficient

Cf - Skin friction- resistance coefficient
:Cp _{- Prismatic coefficient}

Cr - Residuary resistance coefficient

Crough - Roughness resistance - Stimulator resistance coefficient-

coefficient-- CT Total resistance cöefficient for full scale ship

Total- resistance cóefiicient for model without Stimúlator or prototype ship without roughness

cts - Total resistance coefficient for model with stimulator

Ci,. -

### Viscosity

_{resistance coefficient}--- Wave resistance coefficient

d Mean dra'ft of modél or ship Cm):

Stimulator diameter

### Cm)

Fr - Froude NumberF.W. - Fresh water

g - fall acceleration (rn/see2) h - - Depth of towing tank Cm)

### VI

1g Logarithm to base 10

L - Lengh of model or ship at W.L Cm) Lp .- Parallel middle body length (m)

1 - Lengh of towing tank Cm)

is -Wettedstimulator length (m) Re. Reynolds.. Number

Rf. friction resistance (Kg)

Rr -:Residuary resistance (Kg)

Rt - Total résistance without stimulatör and.rouqhneasT(:kq

R1. - Total resistance for full scale ship (Kg or Ton)

R Viscosity resistance (Kg)

R

### -Wave resistance(Kg)

S - Towing tank wetted cross section area (rn2) S'.W- Sait ivàtèr

t - témperàture (C°)

- Speed of ship or model Cm/sec)

Xd - Distance Öfstimulator from the stem (m) Bow angle. of waterline,

- Exit angle f waterline

- Wetted surface withöüt appendéges (rn2) - Wetted surface in appendeges Cm2) p - Mass density (Kg séc2/m,)

y - Coefficient of kinematic viscosity (m2/sec) - Form factor

1.. ACKNOWLEDGEMENT

The invesiigat-ion reported hére was conducted as a joint project by the Coastal & Marine Engineering Research Institute and by the. Hydraulics Laboratory of the Technion isel Institute of Technology.

The author Wishes to acknowledge the help and the

contri-bution tothiswork of Professor MichàelPoreh and to

thank him for his critical review of the first steps in

this stUdy. _{Thanks are also due to Professor Mordechai Diskin}

forhis help, remarks and suggestions. The àuthor also

expresses thanks to the staff of Coastal & Marine Enginéering Research Institute, in particular Mrs I Goldfeld,

Mrs O Cohen

### and Mrs M

Eisler for their assistance inpubiishiñgthis report.

The uthòr also acknowledges the finánciál support, recéived from the .Ceritêr Of Absorption in Science, Israel Ministry of Absorption.

ABSTRACT

the purpose of this report is to review the. possibilities of using small towing tanks for determining ship rèsis-tance and to present the method of ship resistañce calcu-lation adopted at the Technion Towing Tank (I.T.T.), which, it is hoped., reduces to a large extent scale effects in the caiculatiön of the resistance of full scäle

_{ships fÑm}

the data of small model tests. _{An approximate method for}the estimatjó,i of ship resistance is also given hereby.

3. INTRODUCTION

The Technion Towing Tank is 48 m long, 2.5 m wide and 1.5 rn

deep. A parabolic beach i installed at the fa end of the tank.

The water level may be set at any desired level up to a depth of 1.5 m to stimulate a prototype operating: in èither deep or shallow water.

The Towin,g Tank is equipped by carriage which was designed and built by Kempf & Remmers, Hamburg, för the double pur-pose of testing small ship rndels and calibrating water

meters... (Fig. 1). .

The maximum speed of the carriage is 3 rn/sec. _{The speedy is}
measured by a slotted disk interrupting an mfra-red light

beam and converting the signal from digital to analog reading. The equipment was built by the Electronics Laboratory of the Environmental and Water Resources Engineering. Program.

The resistance measuring element is _{an electric balance type}
R-35-1 transducer built by Kempf & Remmers, with the straiñ
gauges in full bridge arrangment. _{This arrangement permits}
high precision measurements. _{The rated maximuñi load at. the.}
balance is 20 Kg and the resolution is close to one gram.

Data processing of the model trial results _{was executed by the}
computer ÑOVA -4/s placed on the carriage. _{The method of}

attaching the model to the carriage and some of themeàsurinq

equipment on. the carriage are shown in Fig. 2.

### a

FIG. NO. 1: THE TOWING CARRIAGE

7

### /

4

### t

FIG. NO. 2: THE MODEL ATTACHED TO THE CARRIAGE AND MEASURING

-5-The towing tankis occasionally used for estimating _{the}

total ship resistance using small scale modéls. The
pre-vious testing procedures and _{an example which calculates}
the prototype resistance of the _{Hebe" were described by}
Hoffman [1].

This work outlines the present _{methodof analysis and}

procedures and explàins the _{reasons for the proposed }

chan-ges _{This method will be calledhereafter}

6

4. METHOD OF SHIP RESISTANCE DETERMINATION FROM SCALE.MODELS

4.1 The Conventional Analysis of Ship Resistance

The conventional method of determining experimental esti-mates of the resistance of full sca1e ships i.s based on the separation of total resistance (Rt) into two compônents

(Fig 3):

(i)

1. Frictional resistance (Rf)

### ? Residuary resistance

Equation (.1) canbe transformed into a dimension1es,..form by using.dimensionless coefficients Which-äré obtained by divi-ding the resistance components by py2

where:

- wetted. surface (m2)

V - speed of ship or model (rn/sec) p - mass density (Kg

### séc2fnik).

The resulting Equation is:

= Cf(Re) + C(Fr) (2)

It is assumed that Cf is a function of the Reybolds number (Re) only, and that. Cr is a function of the.Froude numbér only (Fr). The value of C1 fOr srnöoth ship is calculated

'C;

### I5i6

io### 510

### o

f r 0.075 (1g Re### -2)2

. 'model = C ship### r

r C = 0,0004. rough =.0### + C + C

f. r rough,### by hiC-57

at Fr = idem 2 '3### 4 5 7

O'18 024 0.6 9 (Fr), D'IS 0.24 F_{I}

### /

### LCr_..

### CT

### 3

### 4 5

### 7

110### 3:4

:### ,lOeRe

0.6 0.(fr)9 FIG. NO. 3:8-using the ITTC-51 frictioni resistance curve

0.075 (ig Re, -

### 2)2

The modél tests have the same Fraude numbers as that of the, ship and thus.

Crmôdel Cr ship

Using Cf(Re) calculated by Equation (3)'for ship añd.for model we can obtain:

C. ship' = C. model - Cf model cRe model)

hi.p (Re ship) (5)

The hydraulicroughness.of the môdel is negligible, beçause of

the small Reynolds number, whereas the roughness of the full
scale ship is not always negligible and it depends of course on
the finish _{nd maintenance of the ship} _{It is usually assumed}

that even well maintained ships that appear to be smooth have

anadditiönal roughness résistance óf the order of

The total resistance coefficient for a prototype ship (C1) is thus obtained by adding Crough to the value of C. calcu-lated without the roughness contribution

CT = Ct + Crough

Figure 3 illustrates the conventional method application.

The accuracy of the basic division of the total resistance into two components, described before has never been fully determined. However, it is clear that such a formulation is only approximate. One of the objections to this conventi-onal method is the recognition that part of the residuary resistance is also Reynolds number dependent.

Accepting this observation, it follows that using the conven-tional method for the analysis of data collected at small towing tanks could lead to serious errors since the Reynolds Numbers of model are particularly small.

- lo

4.2 Hughes's Method

A different method for calculating of ship resistance from

model tests has been proposed by Hughes [2,3]. This method is based on the récognition that the residuary ship resis-tance (in Equation 1) is composed of the two parts [Fig. 4].

### R =R

r form w

Where:

Rf0 _{- stems form resistance, which depends on the Reynolds}
number,

- stems from the wave resistance, which depends on Froude number.

Introducing this equation into Equation (i) and expressing it in a dimensionless form, leads to the following Equation

### Cf(R)

_{+ Cform(Re) + C(Fr)}

_{(8)}

Hughes assumed that

form is proportional to C and adop-ted the notatíon:

Cf + Cf0 _{= nCf = C} _{(9)}

where:

is the viscOsity resistance coefficient.

### o

HUGHES'S METHOD### Ct=Cv+Cw

c n Cf = const. 0.066 Cf -(1 Re - 2)2 Cmode.1### Ç,

shipat Fr = idem. /### cs

TfT.T. METHOD Ct = Cts -Cs Ct = Cv .+ Cw = n Cf Ti = const. n nit; Cf### (Tg Re-2)2

(hic-57)### Ç,

model.### = Ç, ship at

Fr idem### C =C+C

T t rough A CroJgh 2 3### 4 5

7 IIO 2 3### 4

5. 7 I I0' 2### 3 4

5 T### 110Re

I I 0.18 0.24### '0ß

O.9(Fr)m### 0I8 024

OS### 0.9(Fr)

FIG. NO. 4:HUGHES'S MEIHOD AND METHOD ADOPTED FN TECHNIÖN TOWING

TANK (I.T.T. METHOD) 0F SHIP

11=

12

-The ratió is:

-FC C

f form - V

Cf Cf

which was defined by Hughes and called the form factor, is assumed to be constant at all speed ranges and depends only. on the geometrical configuration of the ship.

Using this notation, Equation(8)can be réwritten as:

C = TICf(Re) + C(Fr

Hughes proposed the following expression. for C

0.066 ughes

= (1g Ré

### 2)Z

### and suetéd, that the fo

factor r be determined fróm mode.itests at Fr + 0.. -It is known that. at small values of thé Froude Number the wave resistance is negligible. and thé res-i.stance is due to frictional and fôrm resistance

The expressions proposed by Huqhes for the frictional

resist-ance was not accepted-internatiOnally, although itis 1ear

that the baic approach proposed by Hughes has many advantages.

n-- 13

### 4,3

The LMethodMopted;.in:Technion Tówing.tank:(t.T.T.Ïnèthod)Predictión of. ship resistance through the conventional.
analysis of model tests leads to exaggerated values of
Ct as a consequence of the scale effects. _{This errôr}
is considerably greater for small scale models, and
thus special attention to this problem has to be given
in the I.T.T. tests.

Foli.owing:Hughes, the calculation of the ship resistance is based .òn the subdivision of thè

total resi,stance'.;(C) of the prototype and models into three parts (Equatìon(8) and (9). ):

= Cf(Re) + Cf _{Re) + C(Fr)} _{=. nC.}
+ C

Following the conventiOnal analysis, the friction

resist-ancefor model and ship is estimated Using _{the IITC-57,}

Equation (3) ..

O.075. (1g Re - 2)2

The foñu factor r defined by Equatiön (TO)

### Cf(Re) + Cf0(Re)

C,,Cf(Ré)

is assumed to be constant for all speeds;

_{and istheÑfore}

determined from the model tests at low Froude Numbers..
14

-For sharp bottom ships (C < 0.55) , the value of r is

determined at Froude numbérs in the range of 0.1:5 < Fr < 0.2 and for full bottom ships its value is determined at

Fr = 01 [4J.

The Equation (8) dQes not include an allowance for the prototypé roughness and thùs

= C _{+ trough = nCf} 1. C _{+ .rough}

(13)

The method also requires an additional correction which is related to thé. practice of adding a "trip wire" to model to promote the onset of f Urbulence in the boundary 1.ayer This correction is discussed, in séction 4.5.

Figuré 4describes the varIous contrbutions to thé tötal

15

--4.4 Choice of Model Dirnensiors

The optimal selection of model dimensions presents a corn-plicated problem. The model dimension depends on the size of the towing tank and the required speed. The essential .equirements fòr sea going ships are :'!unrestricted. water

depth",.and élimination of influence of the side walls of

the towing tank on the wave system produced by models up.to th.e highest speed.

It is generally agreed, Van Lamern [5], that for models of

relatively slow ships, a tank having awettéd cross sectiOn

area (S) of .100-times the wetted midshipsection area of the model* (Am) will bé sufficient

### A <O.01S

(14)Braun [6] gives an excellent panoramic descriptiqnof the

pre-sentsituatión of the small model towing tank in the World,

including the methods and criteria ofits operations.

Thé classification proposed by Brauntakes.asá

### basis.thequo.-tiént of two Froude Numbers versus the cross

section of the towing tank (S). The two. Fröûde Numbers are : a number basedOn the model ienth (L) and the maximum speed of the towing

- V'max

### vt

and the Froud Number using the cross section (S) and the

maximum speed (V max).

V'max

In the majority of currentl.y working towing tanks, the quotient formed by thèsè two numbers satisfies the condition:

> 0.9

16

Another, criterion for model choice was giVeñ by Voytkunsky [4;7). The criterion., illustrated inFig 5, givestF rela-tive módel' size versus the greatest F.roude Nûmber which must be.achieved in model tests. This determines the model dimen-sions for which the influence of finite tank size is small Minimál acceptable values of ratios of tank width (b) torflodel breadth (B) and tank depth (h) tò the mödel draft (d.) can be estimated from the diagrams in Fig. 5.

(15)

(1 6)

b/B 16

### '4

12 I0 .8### h/d

25### 20

### '5

Io### 02

### -

17### -02

OE3 0.4 0.5 Q3### 04

### 05

### h /dt25

0.6FIG. NO. 5: RELATIVEMODEL SIZE AND TOWING TANK VERSUS

- .18

-Considering. dimensions of Technion Towing Tank:. length (1) 48 m. width (b) - 2.5 rn , depth (h) - 1,5 rn:

a) Criterion of Van Lamern [5)

### Am < 0Òl S

givesA

### <0.01 x2:5x1.50.0375m2

rn

Criterion of Braun [63 L < 1.23 v'gives:

L <.123 /2.5

### x 1.5

2..38m.Criterion of Voytkunsky [4;7] (see Fig. 5) gives For: Fr = 0.3 (for example)

### h.

### e

### 1.5m

; d <

### = 0.167m

b 2.5

### 0.25m

Usually in T.T.Î. for moderate speed ships (FrouderNumber < 0.35 , models of abOUt l.8 2,:3 m. 1ergth are Used.

11f greater values of Froude Number are required, the model length should. be deò'easèd.

4.5 !rjp Wir&' Problem

Testing at small Reynolds Number makes it necessary to ensure early

transmission of the model boundary layer to the turbulent regime. It is customary to use a stimulator in the form of a "Trip.Wire

located at approxirnatory 5% of the length at the modél _{from the stém.}
The diameter of "Trip Wire" is calculated by. a semi-empirical formula
of Koziov L. [4;7]:

where:

ds -

_{stimulatordiamete(m).}

A1 - _{coefficient given in Fig.} _{6 as function} f _{bow}
angle at watérline.

### (ad)

Xd - _{distance of stimulatOr from the stem (m)}
Re - model Reynolds Number

### L

model length (m) 2O### -

19### ___. I

### -r

### I

### ____. I

-15### 20 30 40 o6oa

(19) Fi gUnfortunately, the "Trip. Wire" has its Own drag and it. is advised
to subtract the additional drag of the wire from _{thetptal model}
drag..

Kozlov L. has proposed also an semfempirical _{formula.according to}
which this additiönal _{drag coefficient is:}

- V

### [--.+

0.6]### Sfl

_{(}Xd Xd )

### {2)

where:; d Vred### Re tSifl (

### fr i..

### JV

_{Xd}s') 20

### -.

i _{wetted stimulator length .(}
)

- stimulator diameter (rn)

wetted surface Without appendagés (m2)
- distance of stimulator from the stem (m)
L _{- model length (m)}

V - model 5peed (m/sec)

Rem_ model Reynolds Ñtimber t - . temperature,(C°)

y -, coefticient Of kinematic viscosity (m2/sec)

Total . resistance coefficient of model

### -

21APPROXIMATE METHOD OF SHIP AND MODEL RESISTANCE CALCULATION

5.1 Estimation.of Form Factor

Viscous part of resistance is given by expression (9)

C, = .r Cf

whéré ri is form factor, which is determined by model test at low, speed.. If turbulent boundary layer can nt be obi ained at this lów speed, i.e. low Reynolds Number, form factor n can be calculated approximately. Theoretical calculation of n is also desirable for the control of experimental

resu-its and fOr preliminary ship design.

As a. rèsuit of theoretical investigation of boundary layer and tests conducted on big models, method for empirical estimate. of viscous drag coefficient was developed by Droblenkòv V. [41.

The value öf n can be expressed as a function of threè factors

(Fig. 7): .

where:

L2 1.0 1.0 6.0

### n =

ii K1 K2 70.### 80

22### -90

L### FIG. NO. 7: DETERMINATION OF

'77_{COEFFICIENT FOR TURBULENT}FLOW ABOUT THE SHIP AND MODEL BOb'í.

IO L

### 095ao

1.05 1.00### 25

3.0### 35

B d 0.I### 02

0.3 L- 23

-pri stha:tfc coefficient.

L .-

### lengthofodei of ship ätwaterline (rn)

V - under water volume of ship or model (rn3) K1

-B - - _{breadth of model or ship at Water line (}

)

mean draft (m) L

V

### -t.

24

5.2 Estimation of Wave Resistance

For preliminary calculations ánd test control empirical expression for wave resistance was given by Paprnèi [8]:.

- V2 (23).

where:

displácement (tOn) L -. length of ship (in)

V speed of ship (m/sec)

coefficient representéd in a table

Original fori of. Pa,pmel 's formula was inconvenient for; practical computation. .

Following a proposal by Prof Poreh M this formula was

brought to dirnnsion1ess fpnii _{and the dimensionless empirical}
coefficient was plotted in. Fig. (8): . ..

### --

### Bd_-v

- q. CB - q

where:

q _{coefficient, see Fig. 8, there are in Fig. 8 paramèters:}

Pl ib CB

### r

and r = 1.18 Frblock coefficient

q
0.2 o.I _{0.0}
-Bd

### -v

### LOO

C = q Cß = q -n-= 10 CB t 1.18 Fr V### 7r

0.80 0.75 0.70### 0.654,

### 0.60

k### 0.55

_{050}

### 0.45

### 0.40

### )

### 0.1

### 02

### 03

### 0.4

### 0.5

### 0.6

### 0.7

### 0.8

### Fr

FIG. NO.8:. DETERMINATthN OF- 26

Fr

= Froude's Number

wetted surface Cm2)

- underwater vòlurñe of ship

It is. possible louse t.his method if rr < 1 .2 Fr änd for ordinary hull shape only.

27

-5.3 Calculation Procedure

The Approximate method of ship and model resistance calculation is useful for detection of accidental

err-ors in towing tests and can give resistanceestimatè in

early stages of the ship design.

Tôtai resistance is given by expression:

V2

T

### î

### 2.

where coefficient. of total resistänce

### =C +C +C

y w

_{rough}

Following Hughes viscous resistance is given by Equation (9)

where:

friction resistance coefficient can be calculated by ITTC-57 Equation (3)

0.075

### (lgè- 2)2

and approximate dépendence of r on ship geometry is

- 28

-Coefficient _{n can be expressed as a product of thr?efactors..by}
Equation (22):

(C _{;}

### L)K

(-).K2### (ba)

For wave resistance coefficient _{calculation a modification of}
Paprnel's [8] Equation (4), (see

_{section52),'iaybe used:}

-c Bd B where: Êr) ,' Fig.

The appróximatjon. of _{wave resistancè is valied only if}

1.2 Fr.

The roughness résistance. cOefficient _{is specified as in..section 4.1:}

29

-Then.the: total resistance coefficient

### .-n.

### +c c..

- w rough.

and the total resistance R1:is computed.

### This. methOd can be successfully applied, to ships of

- 30

-6. EXAMPLES FOR THE USE OF THE TT.T METHOD'AND:COMPARISONs'WITH

OTHER METHODS OF RESISTANCE CALCULATION....

6.1 _{Available Data}

The applicability of the I.T.T. method of _{ca"lcula:ting ship}

resistance from model tests was verified by using 'data avail-'
able for two series of tests. One consisted of results of
model' tests on the geometrically similar "Heb&' _{and °Mol'edet"}
ships'. The second series was that of the _{'well-known tests' on}
various models of 'the 'tVi'ctory" ship.

The Hebe° model was bUilt and tested in'a _{French'Laboratory}

at.a scale of 1:13.44. ' . '

The "Moiedet"model was, built and tested _{at the Techni,on. }
Tow-ing Tank in order to check its' accuracy by Hoffman [ii (19S3)
at a scale of 1:50. Comparison 'of:the '1Hebe" and the "Moledet"
indicates that the "Möledet" lines _{were foned 'by increasing}

all the dimensions of the'"Hébe"by _{a rátio of approximately}

1,4. The second model which will be called the Technion model may
thus be considered also to be a 1:50 model of the "Mo1èdet _{or}
1:35.73 of the "Hebe".

A number of' modEls of the "Victory" ship Were búilt and testèd
at varioUs laboratories [4,9,10,11]. _{The scales of'these modèls}
raned' fróm 1:15 to 1:80' and they. were tested by similar

proce-dures as part of a program initiated, by the ITTC. _{The results bf'}
these tests were published 'by Van Manen and Lap in 1955'.'flo].

cs

### -

VLThe results are presented in Table

### 2.

Friction resistance coefficient _{Cf was calculatednext, according}
to the cönventionàl method by iTTC-57 Equation (3);:

0.075

### (lgRe -

### 2)2

### -

31-6.2

_{Shi"Heb ;ResistaflceCalcüiation.usjngT.TT}

_{Method}

In this section the values of ship "Hebe" resistance are
om-puted by the 'T.T.T. method using the outcome of the Technion
and French model tests. _{The data used were taken from the}
report of Hoffman [1]. _{The characteristics of. the prototype}
"Hebe" and of its two models _{are given in Table 1.}

Hoffman calculated resistance for ship "Hebe" Using conventi-ona.1 methòd.

Data ofTechnion model with "Trip Wire" _{stimulator was taken}

from Hoffman's report (p. 51), (Fig. _{9).}

First, stimulator. additional resistance _{coefficient was }

cal-culated byEqúation (2Q):

### r

### 2.6

### q-e

### u

### e

-o### u

0.15o - Cq - Technion Model tests _{from Hoffman's report} _{Cf}

- Computation by hIC-57 Equation

C, - Values of C _{computed by T.TfT. method} _{,C} _{- "Trip} _{Wireil Correction., compUted by Koziov'}

W _{S}
Equation
C

### =C

### -AC

t ts s C n### =

### at Fr = 0.2

n = 1.226 f C, = 1.226 Cf### A

= C.t - C### cw

### _-'-A.

L### I

### "w

2.101 -- -o,### 0.2

_{0.25}

_{0.3}

### Fr

### --3

10 A I I I -4### 1-2106

### .8i06

3.106_{3.5I0}

_{4IO}

### 4.5l0RB

### FIG NO. 9:

_{COMPUTATION 0F MODEL RESISTANCE .tOEFFrCENT BY I.T.T. METHOD USING OUTCOME 0F TEÇMNIOI4}

MODEL TESTS

### C

- 33

-The value of the form factor r can be determined from analysis of experimental data at Fraude Number, where wave resistance is: absent.

Analysis of data for both models shows that the wave resistance

becomes significant for Fröude Number > .2.:(This agrees with

reference [4] recommendation fOr sharp bottomed ship, where

= 0.555. The block coèfficient of those rnodeis equals 0.529).

The form factor r can be. calculated from data for the point

Fr 0.2.

Follöwing: Hughes:

= Cv _{Fy} _{= 0.2 (C.= O)}

Next., itis possible to compute viscous resis.taflcecoéfficient' for all range Of model speed (Equation (g)):

The coefficient of wave resistance was separated by the follow-ing Equation

- 34

-The computations for Technion Model results are shown in Table 3

and in Fig. (9). The same calculation was performed for the French Model (data of model test was taken from Hoffman's report (p. 49)). The results for French model are shown in Table 4 and in Fig. (10).

Comparison of the results presented in Fig. (9) and Fig. (10), shows that values of the wave resistance coefficient Ç, for the French and for the Technion models are practically the same. It is now possible to perform calculations of the total resist-ance for the ship "Hebe". The calculations are given in Table 5.

The friction resistance coefficient (Cf) was calculated according to ITTC-57 for the Reynolds Number of the ship.

The total resistance coefficient (C1) was computed by Equation (13)

C = C + C + C

T y w rough.

The viscosity resistance coefficient (C Cf) was cômputed using
the value of _{found from model tests for Technion and French}
model correspondin9ly.

The wave r-esistance coefficient (Ç,) taken from model tests for the same Froud Number.

The roughness resistant coefficient taken by Equation (6)

(Crough = 0.0004) accordThg to conventional method (section 4.1).

Finally, the total resistance (R1) was computed for various values of the ship speed by:

2

D

### - r'

### o

### I,

2 iÔ

o - C - French model tests from Hoffman's report

### H]

A

### -

### -

vaiues of C, computed by I.T.T. MethodCf - computatiOn by ITTC-5:7 Equation

C n.

### at

Fr 0.2### f

n = 1. 16. Cv = i .### 16 Cf

### C'

### -2iO

C = C### - l.16

Cf -V 77 C - I### I

- i . -_i -.### I-810'

### 9I0'

1010'### I2I0

I3.IO I41O- 36

-The results are plotted on Figs. 11,12

The results of computations for ship on basis of Technion model (L = 2.338 m, A = 35.73)and French model (L =6.25 m, A = 13.44)

are practically the same. This is as predicated above and it

confirms the approach proposed in the T.T.T. method.

The curves of total resistance for the ship "liebe" from Hoffman's calculation by the conventional method are also plotted on Fig. 11. The total ship resistance obtained by Hoffman from the small Tech-nion model deviates appreciably from the results based on larger French model.

As shown on Fig. 11, the increasing deviati.on of Hoffman's calcu-lation (more for Technion model) is a natural manifestation of scale effect.

For comparison, computations of ship "Hebefl resistance were also

perfonied using the approximate method. The results of this calcu-lation are listed in Table 6 and plotted on Fig. il, together with tte other curves.

As can be seen from Fig. 11, the results of the approximate method agree fairly well with those computed by T.T.T. method.

It follows _{that the approximate method can serve the purpose of}
checking test results and for preliminary design estimates of total
ship resistance.

IS

### e

### 4-10

### u

C### o

### 20

Technion model### A

Frénch### model

IO II 12 13### ¡4

15### 16

.17### V(knot)

FIG. No. li: TOTAL RESISTANCE DEPENDENCE ON SPEED FOR SHIP "lIEBE" (1ength 83m). - 37 -- ' _, ' Conventional mèthòd

### T.Í.T.,method'.

O Techniön### model

French model Approximate### method

### /

- 3M

'C xIO

French model

### 4

_{.3}

Original data for Technión model.

Original data for French .modéi.

Calculation for French model by I.T.T. method

[ using data

4)' Calculation for French model by cönvent.ional methodj for Technion model

5) Calculation for ship Hebe by conventional method. (Technion model).

) Calculation for ship .Heb&' by conventional method

(French model)

Calculation for ship "Hébe" byT.T.T. method (Technion model)

Calculation for ship "Hebe" by I.T.T. method (French model).

### 2".

:

### 56 789l0

### a

### 3

### 4

### 5 6789108

FIG NO. 12: _{TOTAL RESISTANCE COEFFICIENT OF MODELS ANO SHIP "HEBE" (without roughness).}

2

### 3

### 4

5### 6 789l0

- 39

-6.3 Cornpàrison:ofReslstanceCalcûlation Methods using theData ftheFrench and the Technion Módeis

In this section, the French test results arecompared with those of derived from the Technion geometrically similar but smaller

model.

In this example French model is considered to be a ship and the Technion model as the small scale model of this ship.

The calculations were made by three methods namely

The conventional method; The method adopted in T.T.T. The approximate method.

The results, i.e. the values of the total resistance coefficient

are presented in Table 7, and plotted Fig. 12 versus Reynolds Number.

The conventional method gives resistance values that are greater

by about 9% than the results of French model tests. The calcula-tions based on I.T.T. method give a deviation of about 4% and the

approximate method gives results that are about 5% above the test

results.

These findings again demonstrate the advantage of the T.T.T. method

in comparison to the other methods of computation of total ship

- 40

-6.4. Comparison of the I.T.T. Method with the "Victory" Ship

Model Tests

The I.T.T. method was compared with the data available from

the known "tictory" model series. The basic dimensions of

the "Victory" are:

L = 135.6m; B = 18.9m; d = 8.69m ; 1 _{=} _{15020 ton; c} _{= 3165m2;}

CB = 0.674 ; C = 0.682.

Experiments on models of this ship were conducted in several large towing tank [7,8,10,11], using the scales:

A = 1:80 ; A = 1:60 ; A = 1:40 ; A = 1:30 ; A = 1:24 ; A = 1:15 (See Fig. 13).

Form factor for "Victory" was computed (see Table 8) at
Fr = 0.15 since hull fullness is rather large (CB=0.674 _{,}

C0.682). Note that the "Hebe" ship has the following

coeffi-cients CBO.S29 , C=0.555 and thus r was determined at Fr=0.2.

The comparison was made by computing values of the form factor through a wide range of Reynolds Numbers (1g Re=5,9 7,2)

The value of r through the entire range of Reynolds Numbers remains fairly constant in the range .1.17 to 1.20.

The analysis of the data also shows that only the ITTC-57 ex-pression for the friction coefficient gives a consistent value

### ?i:eá

### Xr.6O

I I_{I}

### Xi :40

### )i:

### 24

### X1:15

FIG. NO. 13: "VICTORY" SHIP MODEL SERIES EXPERIMENTAL RESULTS [10]

L =

### 135.6 m, B = 18.9 m, d = 8.69

m, A = 15020 t,1 =### 3165

m2- Frictional resistance coeffiçient by hiC-57.

- Frictional resistance coefficient by Shlichting and Prandtl formula.

- 42 -.

We have also tried to use _{different expression for Cf such as Hughes}
expression
O.Q66
Cf

### (lgRe-2)2

and S'hlichting_{- Pfàndtl}0.455 (1g Re)Z

It appears however _{, see Fig 13, that only ITTC-57 frictional }

resi-stance curve gives a constant value of n, independent of the model scale.

We have also calculated the forni factor n using Droblenkov [4]
method, see Fig. 7 _{Equation (2Z which gives:}

Clearly the agreement with the values calculated at

F.r = 0.15 _{,} r = 1.17 + 1.20
is very good.

### (C;L)

= (0.682 ; 5.54) = 1.22 K1### (.:)

=. K1(2.17) =### 0.91

### K2 () =

K2(0.08) = 1.03 n = 1.22.- 43

-7. _{CONCLUSION}

This report contains the description of the Technion
Towing Tank (I.T.T.) method for _{the calculation of ship}
resistance from model tests. _{This method is based on}
separate calculation of the various components of the
total ship resistance.

Application of I.T.T. method to practical calculations
is fully explained arid illustrated by several examples,
which show that this method is well _{stilted for ships of}
ordinary geometry.

It may be thus concluded that the _{application of the}
I.T.T. method allows a reduction of the scale effect in
the, model. _{Consequently, It is possible to use small}
scale models in the existing test tank and achieve good

estimates of the full scaleship _{resistance.}

The I.T.T. method which allows the _{use of small, models}
also makes it possible to achieve relatively high Froude
Numbers at moderate absolute speed of ths carriage.

- 44

-APPENDIX i

Procedures of Ship Resistance Calculation Usin the I.T.T. Method.

Surnary of Model Resistance Subdivision:

- The total model resistance determend from the towing test

R1.

r.

-p

- "Trip wire" resistance coefficient

- see Equation 20

Cf - Friction resistance coefficient by ITIC - 57

0.075

C-f

### (lgRe-2)2

Plotting C.c, C5 Cf versus V,Fr, Re (see Fig. 4)

Estimation of i - form factor from these plots

C. _{}

-n at low Froude Number

where C, = O

If such an estimation is impossible Droblenkovrs ExpressIon

- 45

-6; Calculation and plotting C, = x Cf for all ranges of speed

7. Wave resistance coefficient C,

C = (c. - C5) - flCf

- 46

-Calculation of Ship Resfstance

Calculation Cf using ITTC-57 for Reynold's Number of ships.

Viscosity resistance coefficient

C, = iiC. where

r is determined by model tests.

Total resistance coefficient

### CT=C +C +C

y w rough

where

C - from model tests for the same Froude's Numbers

Crough = 0.0004 according to conventional method.

Total resistance versus speed of ships.

- 47

-8. REFERENCES

Hoffman D. "The Technion Ship Model Towing Tank". Report published by the Hydraulic LabOratory of the Technion Israel Institute of Technology . 1963..

Hughes G. "Frictional and Forni Resistance in Turbu-lent Flow and Proposed Formulation for Use in Model and Ship Correlation". Trans. INA.1954. vol. 96.

Hughes G. "The Prediction of Smooth Ship Resistance from Model Data". Trans. INA.1957. vol 99.

Voytkunsky V.1. "Water Resistance to Ship's Movement". Shipbuilding. Leningrad. USSR. 1964 (In Russian).

Van LanBneren W.P.A., Troost L., Koning G. "Resistance, Propulsion and Steering of Ships'

The Technical Publishing Company Stam-Haarlem-Holland 1948

Braun _{K.Th. "An International Panoramic View on the}
Ship Small Model Basin and its Problems".

Technologia Naval. Vol 1. N 3. 1968.

Voytkunsky Y.I., Perchyz R.Y. and Titov IA.

"Ship's Theory Handbook". Shipbuilding. Leningrad USSR. 1960 (in Russian).

Alferjev MY. _{Apropulsion and..Steering of Ships". }

48

-9. Katzrnan Ph.M. Pustoshny A.F.,. Stumpf V.M. "Propiilsion

-i

of sea-going Vessels'. Shipbuildìng.. Leningrad. USSR. 1972: (in Russian).

lQ..VanManen-i.Dr., Lap A.I.W. "Scale Efféct Experiments on "Victory" ship and Models. Analysis -of the Wak Measúre-men on-Mòdel Family and on the Model Boat".

-Tráns.- I.N.A.. 1955. vol 97. p 167 - 245.

### 1.i.

ToWnsin R.L. "Frictional -and Pressuré. Rs-ÎthñceQf. a-"Victory" Model" Trans NECIES 1961.. vol 78. Part 7### -.

### 49

- 50

-TABLE i

CHkRACTERISTICS OF THE PROTOTYPE "HEBE" AND ITS ?DELS

,, ,, Hebe Thchniònii Model French Model A Scale of models - 35.73 13.44 L Length at W.L. ì 83.554 2.338 6.2168 B Breadth at W.L. m 13.3 0.37 0.99 4 Mean draft m 4.27 0.12 0.32

V Volume without appendages m3 2512

### 55x103

1.032### Displaccnt

ton 2577### '56x103

1.062Wetted surface without appendages m2 1190 0.9315 6.588

Wetted surface with appendages m2 1222 0.957 6.765

Am Midship section area m2 54.53 0.0425

### O3O2

OE Entränce angle o 13 13 13

Exit angle o 38 38 _{38}

CB Block coefficient - 0.529 0.529 0.529

- 51

-TABLE 2

ALC1LATION OF "TRIP WIRE" RESISTANCE COEFFICIENT FOR

### TEC}IIIONJ4ODEL (Equation (20))

/ = 2.. 338 in i = 0.25 in s d = 0.32" = 0.8 X iO3m s Q . 0.9315 in2 Xd = 0.05 L### t°=25°

2### =0.8575 x io6L_

### sec

### Vm

### rn/sec

### Re.

### 106

io-3 0.860 2.36 0.059 0.958 2.63 0.064 1.027 2.82 0.067 1.18.5 2.98 0.0,70 1.145 3.14 ' 0.073### 1.54

3.44 ' 0.077### U30

3.78 0.082'. 1.440 3.96 0.085 1.542 4.23 ' 0.089 'NL

### 2.338m

t

### =27°C

TABLE 3

COMPUTATION OF WAVE RESISTANCE COEFFICIENT AND n FORM COEFFICIENT FOR TECHNION MODEL

pF.W. = 101.6Kg sec2/ni = O.8575x106m2/sec 0.075

### Cf-bYITTC-57

;### Cf_(igR2)2

C - AC = ( ts s -'-Original data for Technion model

from Hoff nnn's report [i]

C C = n Cf

### 'FrO.2

### C. C- AC8 - rlCf

### m/sc

Fr_ C io-e R = Cf io (Table 2### Ct_AC

### io3

### C=flCf

= io### 106

_{}

lo-1 2 3 4 5 6 7 8 9 10
0.86 0.179 4.995 2.36 3.922 0.059 4.936 1.258 4.809
-0.958 0.200 4.771 2.63 3.839 0.064 4.707 1.226 4.707 0
1.127 0.214 4.762 2.82 3.787 0.067 4.695 1.230 4.643 0.052
1.085 0.226 4.880 2.98 3.746 0.070 4.810 1.284 4.593 0.207
1.145 0.239 4.782 3.14 3.699 0.073 4.709 - 4.535 0.160
1.254 0.261 4.870 3.44 3.644 0.077 4.793 - 4.468 0.325
1.380 0.288 5.020 3.78 3.579 0.082 4.938 - 4.388 0.550
1.440 0.301 5.190 3.96 3.548 0.085 5.105 - 4.35Ó 0.755
1.542 0.321 5.470 4.23 3.504 0.009 5.380 - 4.296 1.084
TABLE 4

COMPUTATION OF WAVE RESISTANCE COEFFICIENT AND _{n} _{FORM COEFFICIENT FOR FRENCH MODEL BY T.T.T. METHOD}

= 6.2168 in t° = 15°C pFw = 101.87 Kg sec2/m' y

### = 1.1413106m2/sec

C = C - C = C. - r C 0.075 Cf by ETTC - 57 ; Cf = (1g Re - 2)2 C t### n =(-ç)

_{Fr=O.2}= 1.16 ; C

### = n C

V fOriginal data for French model from

Hoffman's report [i]

W L V L L Vm rn/sec VL Fr= ---- C -t 10 Re- c f

### '5

### io3

C ul Cf = 1.16 Cf C = Cf### io3

y### 106

1 2 3 4 5 6 7 8 1.55 0.200 3.60 8.50 3.10 1.16 3.60 0 1.68 0.216 3.61 9.18 3.045 1.185 3.53 0.08 1.824 0.234 3.67 9.94 3.003 1.200 3.48 0.19 1.96 0.252 3.76 10.72 2.965 T 3.42 0.34 2.10 0.269 3.81 11.50 2.928 - 3.40 0.41 2.24 0.287 3.95 12.22' 2.899 - 3.36 0.59 2.38 0.305 4.10 13.03 2.867 - 3.32 0.78 2.52 0.323 4.29 13.78 2.839 - 3.29 1.00 2.66 0.341 7.74 14.58' 2.814g - 3.26 1.48TABLE 5

CALCULATION.ÒF _{TOTAL RESISTANCE FOR SHIP "HEBE" BY T.T.T. METHOD USING DATA OF TECHNION AND FRENCH MODEL TRIALS}

L

### = 83.554m

Q 1..222m2 t; = 15°C PS.W =. 104.61 Kg sec2/m' = 1.1907 X_{106m2/sec}C

### =.O.4x103

rough C by model tests r. - by model tests 0.075 Cf -. by. ITTC - 57, Cf - (ig Re 2)2### CYÌCf

### C =C+C+C

T### .v w

rough pv2 RT - CT_{2}Li Òrïginal data report from Hoffman's [.1] .

. Recomputation based on Tchnion model

test data from Table 3 _{n} 1.226

Recomputation based on French model

test data from Table 4 n = 1.16

knots

### Re=

10 C by ITTC . 1O C nC = 1.226 Cf 10 C (Fig. 9) 1O C =### ®O.4

iO RT Ton### C =C

l.l6.Cf i0 G (Figo 10) 'i0 C### ®®0.4

10 R Ton 1 2 3 4 5 6 7 8 9 10 11 12 12 .0.216 1.702 2.11. 0.065 r 2.57 . 6.23 1.97 o.O 2.45 5.94 13 0 234 4 700 1 685 2 07 0 14 2 59 7 47 1 96 0 19 2 55 7 35 .14 0.252 5.060 1.669 2.05 0.24 2.69 8.95 1.94 . 0.34### 268

. 8.90 15 0 269 5 430 1 654 2 03 O 37 2 80 10 68 1 92 0 41 2 73 10 40 16 . 0.280 5.785### 164O

2.01 0.55### 296

### 12.5

.1.90 .0.59 . 2.89 . 12.53 17 0 305 6 150 1 627 1 99 0 80 3 19 15 65 1 89 0 78 3 07### 10o

18 0 323 6 510 1 616 1 98### 108

3 44 18 50 1 88 1 00 3 28 17 61 19 0 341 6 870 1 604 1 96 - -_{-}

_{1 86}

_{1 48}

_{3 74}

_{22 86}

¿ : dm = 4.27 V

### =2512m3

=### C. = 0.529

CALCULATION OF TOTAL RESISTANCE

TABLE 6 APPROXIMATE METHOD

### --.= 6.14

### Pr=1.18FrVT

- 0.84 *FOR SHIP "HEBE" USING

### m

_{RT=Rv+Rw+Rrough}m C

### c.=n

Cf Cf ITTC= K1 K1 =(C K1( =1.003 2 i ) n=1.147"I.003>(1 1.15 K.1 °_{p}n =1.147 Fig. 7 K2 CB

### k'°

### f

### c

= (1g Re- 2)Z Knots Fr = V Re= 10 - Cf by ITTC-57 io r### 1.18 FrVÇ

(pr) Fig. 8 C 10### CT=nC +C +Cr

### 1.15 4.++ 0.4

i0 RT=CT .2!_### 16.92002

Ton 1 2### .3

4 5 6 7 8 9 10 0.18 3.621 1.744 0.20 0.003 0.073 2.479 4.19 11 0.198 3.982 1.722 0.22 0.006 0.147 2.527 5.17 12._{0.216}

_{4.345}

_{1.702}

_{0.24}

_{0.011}

_{0.270}

_{2.627}

_{6.40}13 0.234 4.700 1.682 0.26 0.017 0.418 2.752 7.87 14 0.252 5.060 1.669 0.28 0.021 .0.517 2.836 9.41 15 0.269 5.430. 1.654 0.30 0.027 0.664 2.966 11.29 16 . 0.280 5.785 1.640 0.32 0.036 0.886 3.1.72. 13.74 17 0.305

_{6.150}

_{1.627}

_{0.34}

_{0.045}1.107 3.378 16.52 18 0.323 6.510 1.616 0.36 0-062

### L525

. 20.74 19 0.341 6.870 1.604 0.39 0.110 2.706 4.950 30.20 . .CAlCULATION OF TOTAL RESISTANCE FOR FRENCH

### .TABLE7

OF TECHNION MODEL AND APROXIMATE METHOD MODEL USING DATA

. I

I,

Using data of Technion model trials

Original data from

Hoffman's report [i]

for French model

A) The conventional analyslE (4 1) Cf by ITTC-57 B) T T T method (4 3) ri = 1 22 Cf by LTTC-57 C) Approximate method (5 3) n = 1 15 Cf by ITTC-57 u,

### I

Fr Re### 106

CT io C f 1ITTC-57 io C r Technion io### C=

.T### ®

io## Y...

### C.

y io### l22GTechnion

C io### C=

T### ®,.®

io C y### ®

Fr I### I.

-q. (Fig 8 c w Eqs 24 1O### C=

T 10 1 .2 3 4 5 7 8 9 10 11 12 r 13 . 14 0.2 8.5 3.6 3.100 0.87 . 3.97### 378

. 0 3.78. 3.56 . 0.216 9.18 3.61 :3Ø45 0.92 3.96 3.71 0.065 3.78 3.50### O244

0.01.1 0.27 3.77 O 234 9 94 3 67 3 003 0 98 3 99 3 66 0 14 3 80 3 45 0 264 0 017 0 418 3 87 0.252 10.72 3.76. .2.965 1.09 4.06 3.62 0.24. 3.87 . 3.41 0.284 0.021 0.517 3.93 0.269 11.50 3.81### 2928

1.20 4.13 3.57 0.37 . 3.94 3.37 0.305 .0.027 0.664 4.03 O 287 12 22 3 95 2 899 1 41 4 31 3 54 0 55 4 09 3 33 0 325 0 036 0 886 4 22 0 305 13 03 4 10 2 867 1 49 4 36 3 50 0 80 4 30 3 30 0 345 0 045 1 107 4 41 0 323 13 78 4 29 2 839 1 94 4 78 3 46 1 08 4 54 3 26 0 366 0 062 1.525 4 79 0.341 14.58 4.74 2.814 '3.4### 3.3

.. .I)

### À=

L mödel. L ship = 15020 ton L = 135.6 m d = 8.69 m B = 18.9 m TABLE 8COMPARISON OF FORM COEFFICIENT r COMPUTED FOR MODELS IN.WtDE RANCE OF REYNOLDS NUMBERS

USING EXPERIMENTAL OUTCOME OF "VICTORY" MODEL SERIES [io]

II) C - model trial outcome IV) r =

Ship "Victory"

III) Cf - computed by ITTC - 57

f
G 3165 m2
CB= 0.674
C = 0.682
p
r -
-I 1/80 1/60 _{1/40} _{1/30} _{1/24} _{1/15}
II C x 10
(F 0.15) 5.75 5.2 4.55 4.20 3.9 3.5
III Cf )<